Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Theme

The thread: Everything happens in a thin layer

Viscosity is negligible almost everywhere and decisive in a film a millimetre thick, and that film decides drag, stall and the wake.
separatedrecirculation 0.56 Dviscous flow, solved on a coarse grid — the bubble is under-resolvedRe = 40 Viscosity

Everything happens in a layer you cannot see

Air has so little viscosity that ignoring it works almost everywhere. Almost everywhere leaves out a film next to the surface, perhaps a millimetre thick, and that film decides drag, stall and whether an aircraft flies at all.

 creepingattachedseparated, sheddingturbulentbacterium swimmingshedding begins, Re ≈ 47a thrown ballan airliner winga whaleReynolds numberinertia ÷ viscositylog₁₀ Rethe ratio decides the regime, not the size or the speed alone Regimes and numbers

One number decides which physics applies

A bacterium and a whale both swim, and they are not doing the same thing at different sizes. The ratio of inertia to viscosity separates them, and crossing it changes the rules rather than the magnitudes.

 thin: streamlines, frozen at one instantthick: the path one particle actually takesunsteady flow — the three families differincompressible Flows and fields

Streamlines are not the paths particles take

Three different curves get drawn through a flow and they are routinely treated as one. In steady flow they coincide, which is why the confusion survives; in unsteady flow they are as different as a photograph and a long exposure.

 separatedrecirculation 1.16 Dviscous flow, solved on a coarse grid — the bubble is under-resolvedRe = 100 Viscosity

When the flow lets go

Every body asks the air behind it to slow down and climb back up to the pressure it started at. Sometimes the air cannot, and the moment it refuses is separation — the source of most drag, the cause of stall, and the reason a golf ball has dimples.

 Bernoulli holds…along one streamline, steady, inviscid, incompressiblethe theorembetween two different streamlinesneeds irrotational flow as wellthrough a fan, pump or propellerwork is being done on the fluidinside a boundary layerviscosity is the whole story thereacross a shockentropy rises; total pressure does not survivethe hypotheses, not the algebra, are what fail What is taught wrongly

Where Bernoulli's equation applies

The equation is right. Its hypotheses are strict, and almost all misuse is a correct formula carried somewhere it does not hold — across streamlines, through a fan, or into the one layer where friction is the whole story.

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